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So, the dollar growth rate in sales is:
20. To find the new level of fixed assets, we need to find the current percentage of fixed assets to full
capacity sales. Doing so, we find:
Fixed assets/Full capacity sales = $620,000/$588,889
21. Assuming costs vary with sales and a 20 percent increase in sales, the pro forma income statement
will look like this:
Pro Forma Income Statement
Sales $ 1,069,920
Costs 873,480
And the addition to retained earnings will be:
Addition to retained earnings = $125,699 – 44,204
Addition to retained earnings = $81,495
The new retained earnings on the pro forma balance sheet will be:
New retained earnings = $174,730 + 81,495
The pro forma balance sheet will look like this:
Pro Forma Balance Sheet
Assets Liabilities and Owners’ Equity
Current assets Current liabilities
Cash $ 29,136 Accounts payable $ 78,240
Accounts receivable 44,484 Notes payable 16,320
22. First, we need to calculate full capacity sales, which is:
Full capacity sales = $891,600/.80
Full capacity sales = $1,114,500
The full capacity ratio at full capacity sales is:
23. The D/E ratio of the company is:
D/E = ($81,520 + 155,000)/$304,730
D/E = .7762
So the new total debt amount will be:
New total debt = .7762($386,225)
The pro forma balance sheet with the new long-term debt will be:
Pro Forma Balance Sheet
Assets Liabilities and Owners’ Equity
Current assets Current liabilities
Cash $ 29,136 Accounts payable $ 78,240
Accounts receivable 44,484 Notes payable 16,320
Fixed assets
Net plant and Owners’ equity
equipment 475,800 Common stock and
paid-in surplus $ 130,000
Retained earnings 256,225
Total debt needed = .44($649,500) = $283,824
Equity needed = .56($649,500) = $365,676
So, the repurchases of debt and equity will be:
Debt repurchase = ($94,560 + 205,213) – 283,824 = $15,949
Equity repurchase = $386,225 – 365,676 = $20,549
Pro Forma Balance Sheet
Assets Liabilities and Owners’ Equity
Current assets Current liabilities
Cash $ 29,136 Accounts payable $ 78,240
paid-in surplus $ 130,000
Retained earnings 235,676
Total $ 365,676
24. The pro forma income statements for all three growth rates will be:
Pro Forma Income Statement
15 % Sales
Growth
20% Sales
Growth
25% Sales
Growth
Sales
$1,025,340
$1,069,920
$1,114,500
the dividends paid will be:
Dividends = ($36,224/$103,007)($120,026)
Dividends = $42,209
And the addition to retained earnings will be:
Addition to retained earnings = $120,026 – 42,209
The pro forma balance sheet will look like this:
15% Sales Growth:
Pro Forma Balance Sheet
Assets Liabilities and Owners’ Equity
Current assets Current liabilities
Cash $ 27,922 Accounts payable $ 74,980
Accounts receivable 42,631 Notes payable 16,320
Inventory 95,910 Total $ 91,300
Total $ 166,463 Long-term debt $ 155,000
Fixed assets
Net plant and Owners’ equity
At a 20 percent growth rate, and assuming the payout ratio is constant, the dividends paid will be:
Dividends = ($36,224/$103,007)($125,699)
Dividends = $44,204
And the addition to retained earnings will be:
Addition to retained earnings = $125,699 – 44,204
The pro forma balance sheet will look like this:
20% Sales Growth:
Pro Forma Balance Sheet
Assets Liabilities and Owners’ Equity
Current assets Current liabilities
Cash $ 29,136 Accounts payable $ 78,240
Accounts receivable 44,484 Notes payable 16,320
Inventory 100,080 Total $ 94,560
Total $ 173,700 Long-term debt 155,000
Fixed assets
Net plant and Owners’ equity
At a 25 percent growth rate, and assuming the payout ratio is constant, the dividends paid will be:
Dividends = ($36,224/$103,007)($131,372)
Dividends = $46,199
And the addition to retained earnings will be:
Addition to retained earnings = $131,372 – 46,199
Accounts receivable 46,338 Notes payable 16,320
Inventory 104,250 Total $ 97,820
Total $ 180,938 Long-term debt $ 155,000
Fixed assets
Net plant and Owners’ equity
25. The pro forma income statements for all three growth rates will be:
Pro Forma Income Statement
20% Sales
Growth
30% Sales
Growth
35% Sales
Growth
Sales
$1,069,920
$1,159,080
$1,203,660
Dividends = ($36,224/$103,007)($137,044)
Dividends = $48,194
And the addition to retained earnings will be:
Addition to retained earnings = $137,044 – 48,194
Addition to retained earnings = $88,851
Sales growth rate = 30% and debt/equity ratio = .7762:
Pro Forma Balance Sheet
Assets Liabilities and Owners’ Equity
Current assets Current liabilities
Cash $ 31,564 Accounts payable $ 84,760
Accounts receivable 48,191 Notes payable 16,320
So the excess debt raised is:
Excess debt = $699,063 – 703,625
Excess debt = –$4,562
At a 30 percent growth rate, the firm will need funds in the amount of $4,562 in addition to the
New retained earnings = $174,730 + 92,529
New retained earnings = $267,259
The new total debt will be:
New total debt = .7762($397,259)
New total debt = $308,337
Pro Forma Balance Sheet
Assets Liabilities and Owners’ Equity
Current assets Current liabilities
Cash $ 32,778 Accounts payable $ 88,020
Accounts receivable 50,045 Notes payable 16,320
Inventory 112,590 Total $ 104,340
Total $ 195,413 Long-term debt $ 203,997
Fixed assets
Net plant and Owners’ equity
equipment 535,275 Common stock and
paid-in surplus $ 130,000
26. We need the ROE to calculate the sustainable growth rate. The ROE is:
ROE = (Profit margin)(Total asset turnover)(Equity multiplier)
b = 1.38
This implies the payout ratio is:
Payout ratio = 1 – b
Payout ratio = 1 – 1.38
27. We know that EFN is:
EFN = Increase in assets – Addition to retained earnings
The increase in assets is the beginning assets times the growth rate, so:
Increase in assets = A g
28. We start with the EFN equation we derived in Problem 27 and set it equal to zero:
EFN = 0 = –PM(S)b + [A – PM(S)b]g
Substituting the rearranged profit margin equation into the internal growth rate equation, we have:
Internal growth rate = [PM(S)b]/[A – PM(S)b]
29. In the following derivations, the subscript “E” refers to end of period numbers, and the subscript “B”
refers to beginning of period numbers. TE is total equity and TA is total assets.
For the sustainable growth rate:
Sustainable growth rate = (ROEE × b)/(1 – ROEE × b)
Sustainable growth rate = (NI/TEE × b)/(1 – NI/TEE × b)
Since ROEB = NI/TEB
The sustainable growth rate equation is:
Sustainable growth rate = ROEB × b
For the internal growth rate:
Internal growth rate = (ROAE × b)/(1 – ROAE × b)
30. Since the company issued no new equity, shareholders’ equity increased by retained earnings. Retained
earnings for the year were:
Retained earnings = NI – Dividends
Retained earnings = $80,000 – 44,000
Retained earnings = $36,000
Using the equation presented in the text for the sustainable growth rate, we get:
Sustainable growth rate = (ROE × b)/[1 – (ROE × b)]
Sustainable growth rate = [.2703(.45)]/[1 – .2703(.45)]
Sustainable growth rate = .1385, or 13.85%
The ROE based on the beginning of period equity is
